Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 167

> set.seed(200694)
> X < - as.matrix(cbind(pik,framepop$xc,framepop$yc))
> bal1 < - samplecube(X,pik,comment ¼ TRUE,method ¼ 1)

BEGINNING OF THE FLIGHT PHASE
...
QUALITY OF BALANCING
TOTALS HorvitzThompson_estimators Relative_deviation
pik 100.0000 100.0000 1.406875e-12

2 494.0807 491.0461 -6.141966e-01

3 494.8565 495.9795 2.269404e-01

> sum(bal1)
[1] 100

> framebal < - framepop[bal1 ¼¼ 1,]
> points(framebal$xc,framebal$yc, pch¼1, cex¼2)

In this case, the spatial balance index, SB, is

> spbalance(ds,rep(n/N,N),(1:1000)[bal1¼¼1])
[1] 0.3242424

This high SB value (if compared with the SB values of the designs in the previous
section) demonstrates that balancing the sample on the coordinates is quite different
from the concept of spatially balanced samples (the SB value for GRTS is much
lower).
The algorithm can also use varying

π k s to select balanced π ps samples (see

Fig. 7.4 ).

> set.seed(200694)
> par(mar ¼ c(1,1,1,1),xaxs ¼ "i",yaxs ¼ "i")
> plot(framepop$xc,framepop$yc, axes ¼ F,cex ¼ 0.5,pch ¼ 19,
+ xlim ¼ c(0,1),ylim ¼ c(0,1))
> box()
> pik2 < - inclusionprobabilities(ypps,n)
> X < - as.matrix(cbind(pik2,framepop$xc,framepop$yc))
> bal2 < - samplecube(X,pik,comment ¼ TRUE,method ¼ 1)

BEGINNING OF THE FLIGHT PHASE
...
QUALITY OF BALANCING
TOTALS HorvitzThompson_estimators Relative_deviation
pik2 100.0000 100.0000 -1.136868e-13

2 494.0807 544.4423 1.019300e+01

3 494.8565 525.1639 6.124477e+